Yizhi Yin
School of Mathematical Sciences, Shenzhen University, Shenzhen, China.
DOI: 10.4236/am.2026.175017   PDF         2 Downloads   30 Views   Citations

Abstract

Let F_k be the (friendship) graph obtained from k triangles by sharing a common vertex. In 2024, Li, Lu, Peng [Discrete Mathematics 346(2023)] show that the unique n-vertex F₂ -free spectral extremal graph is the balanced bipartite graph adding an edge in smaller part if n ≥7. Following their result, we show that the unique n-vertex F₃-free spectral extremal graph is the balanced complete bipartite graph adding two disjoint K₃ in the vertex part with smaller size if n > 360.

Keywords

F₃-Free, Spectral Extremal Graph, Balanced Complete Bipartite Graph

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Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

References

[1]	Bondy, J.A. and Murty, U.S.R. (2008) Graph Theory, Graduate Texts in Mathematics, vol. 24. Springer.
[2]	Erdos, P., Furedi, Z., Gould, R.J. and Gunderson, D.S. (1995) Extremal Graphs for Intersecting Triangles. Journal of Combinatorial Theory, Series B, 64, 89-100.[CrossRef]
[3]	Cioab, S., Feng, L., Tait, M. and Zhang, X. (2020) The Maximum Spectral Radius of Graphs without Friendship Subgraphs. The Electronic Journal of Combinatorics, 27, Article No. P4.22.[CrossRef]
[4]	Zhai, M., Liu, R. and Xue, J. (2022) A Unique Characterization of Spectral Extrema for Friendship Graphs. The Electronic Journal of Combinatorics, 29, Article No. P3.32.[CrossRef]
[5]	Li, Y., Lu, L. and Peng, Y. (2023) Spectral Extremal Graphs for the Bowtie. Discrete Mathematics, 346, Article ID: 113680.[CrossRef]
[6]	Chen, Y., Li, S., Zhang, L. and Zhang, M. (2025) Spectral Extrema of F2-Free Graphs with Given Size Revisited. Discrete Applied Mathematics, 375, 294-307.[CrossRef]
[7]	Yu, L., Li, Y. and Peng, Y. (2025) Spectral Extremal Graphs for Fan Graphs. Discrete Mathematics, 348, Article ID: 114391.[CrossRef]
[8]	Gao, J. and Li, X. (2026) Spectral Radius of Graphs of Given Size with a Forbidden Fan Graph F6. Discrete Mathematics, 349, Article ID: 114695.[CrossRef]
[9]	Li, S., Zhao, S. and Zou, L. (2025) Spectral Extrema of Graphs with Fixed Size: Forbidden a Fan Graph, a Friendship Graph, or a Theta Graph. Journal of Graph Theory, 110, 483-495.[CrossRef]
[10]	Zhang, Y. and Wang, L. (2024) On the Spectral Radius of Graphs without a Gem. Discrete Mathematics, 347, Article ID: 114171.[CrossRef]
[11]	Li, Y., Feng, L. and Peng, Y. (2025) A Spectral Erdos-Faudree-Rousseau Theorem. Journal of Graph Theory, 110, 408-425.[CrossRef]
[12]	Hoffman, A.J. and Smith, J.H. (1975) Recent Advances in Graph Theory. Academic Praha.
[13]	Csikvri, P. (2009) On a Conjecture of V. Nikiforov. Discrete Mathematics, 309, 4522-4526.[CrossRef]
[14]	Chvtal, V. and Hanson, D. (1976) Degrees and Matchings. Journal of Combinatorial Theory, Series B, 20, 128-138.[CrossRef]